One form of apparatus for producing hollow bodies from thermoplastic material involves using a mode of operation in which a hollow substantially cylindrical blank which is produced for example by molding and which has a bottom portion is subjected to a treatment consisting of a plurality of steps, in which at least a part of the blank is subjected to a variation in temperature and suitably deformed or shaped. That procedure may involve for example stretching the wall of the blank at a temperature below the vitreous transition temperature of the material forming same to provide an intermediate product or parison which is subjected to preliminary expansion at its open end; then, operating at that open and pre-expanded end, the intermediate product is expanded at least over the major part of its longitudinal extent and then subjected to a thermofixing operation, whereupon the wall portion of the expanded intermediate product, adjoining the opening thereof, is reduced in diameter and a flanged edge is formed at the free end thereof. Hollow bodies of that kind, which are of a generally can-like configuration and which can be used for example for containing beverages which are under an increased pressure within the can-like container are required in very large numbers so that there is a need for the apparatus for making same to be of such a configuration that a plurality of blanks and intermediate products formed therefrom can be simultaneously subjected to the same treatment steps. That presupposes that the apparatus has a correspondingly large number of identical treatment stations which are disposed in parallel relationship with each other.